Shares of the brick and mortar bookseller soared nearly 7 percent Thursday on a report that it was mulling going private — something that activist investor Sandell Asset Management would be surely support.

The New York-based bookseller denied a Wednesday report that it had retained Guggenheim Partners to help it explore a sale. The report by trade publication Deal Reporter also said B&N spoke to private equity firms Apollo Management and Platinum Equity.

“Although we have an obligation as a public company to listen to any proposals or offers from outside parties, we are not engaged in a process at this time,” B&N spokeswoman Mary Ellen Keating told The Post.

The bookseller’s denial didn’t stop the stock from rising: The shares ended up 6.9 percent at $7.75.

B&N has used Guggenheim as its financial advisor for several transactions, including its $600 million spinoff of Barnes & Noble Education in August 2015.

In a troubled retail climate, analysts are hard-pressed to say who would buy it — despite speculation about Amazon, a buyout firm or even a billionaire bibliophile.

“Barnes & Noble would be an interesting asset for someone who loves books but you’ve got to have fundamental angle for how you’d run it better,” John Tinker, analyst with Gabelli & Company told The Post.